Due to certain circumstances, I ran right out of gas and since putting in more gas, the car shakes very hard; doesn't idle propely at all and hardly any power when mashing gas pedal.

I believe that the Gas Filter got clogged with the sedimentary deposits/gunk when tank was low. Does this assunption make sense and how should I resolve it? Already tried fuel injector cleaners twice; should I just clean Gas Filter, or replace it entirely?